Economists had forecast the index to drop to 55.0 from 55.2 in August.
"Growth accelerated in both manufacturing and services, albeit with the former continuing to lead the expansion".
It's thought the eurozone could now see its economy grow by 0.7 per cent in the thrid quarter.
France's service output came in at 57.1, and manufacturing at 56.0.
The services Purchasing Managers' Index increased to 55.6 from 54.7 in August.
Germany's private sector expanded at the fastest pace in nearly six-and-a-half years in September, a survey showed on Sept. 22, suggesting Europe's largest economy is firing on all cylinders before a federal election on Sunday.
France, the eurozone's second-biggest economy, also had a strong reading, providing "more good news for Macron", Berenberg's Hense said, as French President Emmanuel Macron makes a push to implement controversial labour reforms.
Brown at Capital Economics said European Central Bank policy makers may be "emboldened" by the fresh signs of a strong recovery, but markets should not get ahead of themselves given that inflation - a key trigger for rate moves - is set to increase only gradually.
The euro was marked 0.45% higher against a weaker USA dollar in London trading following the data release, suggesting investors are continuing to be that ECB President Mario Draghi will signal an end to the Bank's three-year, €2.3 trillion program of quantitative easing, and negative interest rates, at its next policy meeting in October.
Analysts had expected the reading to slip only to 55.9.
September data revealed a strong increase in US private sector business activity, with the rate of growth close to August's seven-month peak. Businesses benefited from a sharp rise in orders, prompting them to add to their headcount, especially in manufacturing, to deal with a rise in outstanding business. Average growth in the third quarter as a whole was robust but slightly below that seen in quarter two, reflecting the comparatively subdued rate of expansion seen in July.